Fourier Series and Approximations
7.5 ECTS credits- Orthogonal series. Total and complete systems. Bessel´s inequality and Parseval´s identity.
- Trigonometric system. Completeness.
- Pointwise convergence (Dirichlet-Jordan; Dini-Lipschitz; Lebesgue´s tests).
- Lebesgue´s constants. Uniform convergence.
- Summation of Fourier series by Cesaro and Abel-Poisson means.
- Conjugate function.
- Convergence in Lp.
- Series with monotone coefficients. Lacunary series.
- Absolute convergence.
- Fourier coefficients. Hardy-Littlewood, Paley, and Hausdorff-Young theorems.
- General trigonometric series.
- Moduli of continuity.
- Algebraic and trigonometric polynomials. Bernstein and Markov inequalities. Nikolskii´s inequality.
- The error of approximation (Jackson´s theorem). Inverse theorems.
- Trigonometric system. Completeness.
- Pointwise convergence (Dirichlet-Jordan; Dini-Lipschitz; Lebesgue´s tests).
- Lebesgue´s constants. Uniform convergence.
- Summation of Fourier series by Cesaro and Abel-Poisson means.
- Conjugate function.
- Convergence in Lp.
- Series with monotone coefficients. Lacunary series.
- Absolute convergence.
- Fourier coefficients. Hardy-Littlewood, Paley, and Hausdorff-Young theorems.
- General trigonometric series.
- Moduli of continuity.
- Algebraic and trigonometric polynomials. Bernstein and Markov inequalities. Nikolskii´s inequality.
- The error of approximation (Jackson´s theorem). Inverse theorems.
Progressive specialisation:
A1F (has second‐cycle course/s as entry requirements)
Education level:
Master's level
Admission requirements:
Mathematics 60 ECTS cr, including Complex Analysis, 7,5 ECTS cr, and Measure and Integration Theory, 7,5 ECTS cr, or equivalent.
Selection:
Selection is usually based on your grade point average from upper secondary school or the number of credit points from previous university studies, or both.
Course code:
MAAD25
The course is not included in the course offerings for the next period.